8 papers
Maximum Entropy Least Squares Solutions of Overdetermined Linear Systems
Felice Iavernaro, Monica Lazzo, Lorenzo Pisani
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, moti…
A Multi-Order Extension of Fractional HBVMs (FHBVMs)
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro +1
The efficient numerical solution of fractional differential equations has been recently tackled through the definition of Fractional HBVMs (FHBVMs), a class of Runge-Kutta type met…
High-order Gauss-Legendre methods admit a composition representation and a conjugate-symplectic counterpart
Felice Iavernaro, Francesca Mazzia, Ernst Hairer
One of the most classical pairs of symplectic and conjugate-symplectic schemes is given by the Midpoint method (the Gauss-Runge-Kutta method of order 2) and the Trapezoidal rule. T…
On the use of the principle of maximum entropy to improve the robustness of bivariate spline least-squares approximation
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distributi…
Analysis and implementation of collocation methods for fractional differential equations
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro +1
Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential…
Does the fluid-static equilibrium of a self-gravitating isothermal sphere of van der Waals' gas present multiple solutions?
Domenico Giordano, Pierluigi Amodio, Felice Iavernaro +1
We take up the investigation we left in the future-work stack in Giordano \textit{et al.} [``Fluid statics of a self-gravitational isothermal sphere of van der Waals' gas,'' Phys.…